Low-power hall thruster with an internally mounted low-current hollow cathode

ABSTRACT

A low-power Hall thruster gains significantly improved efficiency by a combination of features, including a single piece, h-shaped magnetic screen which enables a more efficient internal volume utilization as well as optimal magnetic shielding; an internally mounted cathode with varying diameter further decreases the footprint of the thruster; an anode with multiple baffles connected by axially oriented holes generates a highly azimuthally uniform propellant flow.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a continuation of U.S. patent applicationSer. No. 16/205,048, filed on Nov. 29, 2018, which claims priority toU.S. Provisional Patent Application No. 62/640,185, filed on Mar. 8,2018, U.S. Provisional Patent Application No. 62/644,728, filed on Mar.19, 2018, U.S. Provisional Patent Application No. 62/645,072, filed onMar. 19, 2018, and U.S. Provisional Patent Application No. 62/595,306,filed on Dec. 6, 2017, the disclosures of all of these beingincorporated herein by reference in their entirety.

STATEMENT OF INTEREST

The invention described herein was made in the performance of work undera NASA contract NNN12AA01C, and is subject to the provisions of PublicLaw 96-517 (35 USC 202) in which the Contractor has elected to retaintitle.

TECHNICAL FIELD

The present disclosure relates to Hall thrusters. More particularly, itrelates to a low-power, long-life, high-efficiency Hall thruster with aninternally-mounted ultra-compact low-current hollow cathode.

BRIEF DESCRIPTION OF DRAWINGS

The accompanying drawings, which are incorporated into and constitute apart of this specification, illustrate one or more embodiments of thepresent disclosure and, together with the description of exampleembodiments, serve to explain the principles and implementations of thedisclosure.

FIG. 1 illustrates predicted electron temperature contours based onnumerical simulations using the 2D axisymmetric Hall thruster plasmamodeling tool Hall2De.

FIG. 2 illustrates predicted plasma potential contours based onnumerical simulations using the 2D axisymmetric Hall thruster plasmamodeling tool Hall2De.

FIG. 3 illustrates the discharge current-voltage behavior of thefirst-generation ultra-compact hollow cathode.

FIG. 4 illustrates an experimental dataset of keeper voltages at whichfield emission was established for the first-generation ultra-compacthollow cathode.

FIG. 5 illustrates the flow response by the pitot probe sensor when thegas flow is terminated at the feedthrough into the vacuum chamber.

FIG. 6 illustrates data on the propellant flow uniformity for the anode.

FIGS. 7-8 illustrate high speed telemetry.

FIG. 9 illustrates an exemplary Hall thruster diagram.

FIG. 10 illustrates an exemplary ultra-compact cathode heater.

FIG. 11 illustrates an exemplary Hall thruster highlighting theone-piece magnetic screen.

FIGS. 12-13 illustrate thrusters according to prior art.

FIG. 14 illustrates the MaSMi-DM cathode's lanthanum-hexaboridethermionic emitter lifetime estimate as a function of discharge current.

FIG. 15 illustrates the operation envelope for the MaSMi-DM performancecharacterization.

FIG. 16 illustrates MaSMi-DM thrust vs. discharge power.

FIG. 17 illustrates a cross section of the MaSMi-DM Hall thrusterhighlighting the anode manifold location relative to the dischargechannel.

FIG. 18 illustrates the anode and baffles.

FIGS. 19-20 illustrate the measured azimuthal propellant distributionfor two anode manifolds.

FIG. 21 illustrates a cross section of the HUD anode with line-of-sightblocking lips added to the downstream end of the anode cap.

FIGS. 22-23 illustrate exemplary rectangular cross section baffles forthe anode of FIG. 18.

FIG. 24 illustrates MaSMi-DM total specific impulse vs. discharge power.

FIG. 25 illustrates MaSMi-DM total efficiency vs. discharge power.

FIG. 26 illustrates MaSMi-DM discharge current oscillations (ratio ofpeak-to-peak current to mean current) vs. discharge current.

FIG. 27 illustrates exemplary baffle cross sections.

FIG. 28 illustrates an exemplary single-piece magnetic screen.

SUMMARY

In a first aspect of the disclosure, a Hall thruster is described, theHall thruster comprising: a center axis oriented from an upstreamsection of the Hall thruster, the upstream section housing a back polefor a magnetic circuit and a supply line for a gas propellant, to adownstream section adjacent to an azimuthally-symmetrical dischargechamber; and a single-piece azimuthally-symmetrical magnetic screen,wherein: the azimuthally-symmetrical discharge chamber has an annularshape, the single-piece azimuthally-symmetrical magnetic screen has anh-shape cross section, the h-shape cross section comprising a firstprong at an upstream end and two prongs at a downstream end, thesingle-piece azimuthally-symmetrical magnetic screen comprises a firsthollow cylinder physically contacting the back pole at a single circularpoint of contact, the single-piece azimuthally-symmetrical magneticscreen comprises a second and third hollow cylinders, the second hollowcylinder being concentric to the third hollow cylinder, and theazimuthally-symmetrical discharge chamber comprises a radially-outwardwall and a radially-inward wall, the second hollow cylinder of thesingle-piece azimuthally-symmetrical magnetic screen encircles theradially-inward wall of the azimuthally-symmetrical discharge chamber,and the third hollow cylinder of the single-pieceazimuthally-symmetrical magnetic screen encircles the radially-outwardwall of the azimuthally-symmetrical discharge chamber, thereby forming amagnetic field protecting the radially-outward wall and theradially-inward wall of the azimuthally-symmetrical discharge chamberfrom erosion due to ion bombardment.

In a second aspect of the disclosure, a Hall thruster is described, theHall thruster comprising: a center axis oriented from an upstreamsection of the Hall thruster, the upstream section housing a back polefor a magnetic circuit and a supply line for a gas propellant, to adownstream section adjacent to an azimuthally-symmetrical dischargechamber; and an internally-mounted cathode along the center axis, theinternally-mounted cathode having a variable diameter, wherein: theinternally-mounted cathode comprises an upstream section and adownstream section, and the upstream section is axially longer than thedownstream section.

In a third aspect of the disclosure, a Hall thruster is described, theHall thruster comprising: a center axis oriented from an upstreamsection of the Hall thruster, the upstream section housing a back polefor a magnetic circuit and a supply line for a gas propellant, to adownstream section adjacent to an azimuthally-symmetrical dischargechamber; and an azimuthally-symmetrical anode within theazimuthally-symmetrical discharge chamber, wherein: theazimuthally-symmetrical anode comprises a plurality of bafflesconfigured to increase azimuthal flow uniformity for the gas propellant,the plurality of baffles comprises at least: a first baffle comprising afirst plurality of holes connecting the first baffle to the supply line;a second baffle adjacent to the first baffle and connected to the firstbaffle through a second plurality of holes; and a third baffle adjacentto the second baffle and connected to the second baffle through a thirdplurality of circular holes, the first baffle is upstream of the secondbaffle, the second baffle is upstream of the third baffle, the first,second and third baffles are azimuthally-symmetrical, the third bafflecomprises a radially-inward surface and a radially-outward surface, andthe third baffle comprises a fourth plurality of holes on theradially-inward and radially-outward surfaces.

DETAILED DESCRIPTION

The present disclosure describes Hall thrusters with severalimprovements in the generation of a magnetically shielding fieldtopology, the propellant flow uniformity, and the internal hollowcathode. Hall thrusters are described comprising one or more of suchimprovements, enabling, in some embodiments, the construction of alow-power, long-life, high-efficiency Hall thruster with aninternally-mounted ultra-compact low-current hollow cathode. In someembodiments, a Hall thruster may comprise only one of the featuresdescribed in the present disclosure, while in other embodiments, morethan one, or even all such features can be incorporated in a single Hallthruster.

In the following, the present disclosure describes the development andperformance testing of a low-power magnetically shielded Hall thrusterwith an internally-mounted hollow cathode. The low current cathodedemonstrated stable current-voltage characteristics and thermalperformance over the operational range of sub-kW Hall thrusters. In someembodiments, the cathode uses a standard sheathed heater to heat thethermionic emitter prior to cathode ignition. However, heaterlessignition testing revealed a predictable start-up behavior and providedinsight into the system-level architecture required for reliableheaterless ignitions. Therefore, in some embodiments, the cathode may beheaterless. An exemplary anode gas feed design used in the Hall thrusterdemonstrated a maximum peak-to-peak pressure variation of 3.2% and 2.6%at propellant flow rates of 1 mg/s and 3 mg/s, respectively. Initialtesting was carried out at 300 V and 500 W in a non-optimized operatingcondition demonstrating 41% total efficiency with a total specificimpulse of 1320 s. Visual observations of the plasma discharge,post-operation observation of the carbon-coated discharge channel walls,as well as the results from plasma simulations provide strong evidenceof magnetic shielding. High speed diagnostics recorded normal breathingmode oscillation behavior in the 20-50 kHz range and captured additionalmodes at frequencies greater than 200 kHz, possibly associated withazimuthal discharge plasma spokes or the cathode.

NASA's growing interest in small, compact satellites, generally termedas belonging to the SmallSat class of interplanetary spacecraft, hasencouraged the development of numerous solar electric propulsion (SEP)technologies, especially low-power Hall thrusters. First developed forflight applications in Russia in the 1960's-1970's, Hall thrusters havebeen flown on hundreds of Earth-orbiting spacecraft and are beginning tobe considered and selected for deep-space scientific missions. Recentmission studies show that a low-power Hall thruster designed forlong-life, high efficiency operation would be enabling forinterplanetary missions using sub-350 kg spacecraft. However,commercially available flight-proven low-power (sub-kW) Hall thrustersare generally limited to sub-50% efficiencies and maximum lifetimes ofthe order of a few thousand hours. For example, BHT-200 is aflight-proven 200 W thruster capable of 11-13 mN of thrust and1,200-1,600 s of specific impulse (I_(sp)) at a total efficiency of30-40% with a total demonstrated throughput of around 6 kg Xe (˜2′,000h). As another example, the 350 W SPT-50 has demonstrated up to 2,500 hof flight operation (˜19 kg Xe throughput) and produces a thrust of 20mN and an I_(sp) of 1,100-1,300 s at a total efficiency of 33-35%. TheSPT-70, a flight demonstrated thruster with a maximum operation time of3,100 h (˜28 kg Xe throughput), produces 40 mN of thrust and 1,450-1,500s of I_(sp) at a total efficiency of 45-48% and a nominal power of650-700 W. Two key commonalities exist between current flight-provenHall thrusters, including BHT-600 and SPT-70: they use predominantlyradial (i.e. unshielded) magnetic field topologies, which limitsthruster lifetime, and they use an externally mounted hollow cathode.

Unshielded magnetic field topologies have been shown to inducelife-limiting ion-bombardment sputter erosion of the discharge channelenhanced by high-energy electron losses to the channel surfaces. Asknown to the person of ordinary skill in the art, magnetic shielding ofHall thrusters has been shown to significantly increase the usefullifetime of Hall thrusters, by reducing the kinetic energy of ions ontrajectories to impact the discharge channel surfaces. The kineticenergy is reduced below the material's sputtering threshold, therebypreventing (or reducing by orders of magnitude) ion-bombardment erosionof the discharge channel. Magnetic shielding can also reconfigure themagnetic field lines, thereby controlling the trajectories of ions andprevent impacts against surfaces. A dramatic reduction in plasma-wallinteractions on both low-power and high-power Hall thrusters,corresponding to up to a 1000× increase in life and no significantdetriments to performance, has been computationally and experimentallydemonstrated.

Hollow cathodes used in flight Hall thrusters of all power levels havetraditionally been mounted externally to the thruster's magneticcircuit, as is the case for all of the flight thrusters mentioned above.In lower-power thrusters, this is primarily due to the lack of spacealong the thruster centerline axis to simultaneously accommodate aninternally-mounted cathode and generate the desired magnetic field.Studies comparing externally and internally mounted hollow cathodes onmid and high power thrusters have demonstrated higher performance andefficiency, reduced discharge oscillations, improved cathode-thrustercoupling (i.e. lower cathode-ground voltage), improved plume symmetry,and decreased beam divergence (i.e. improved thruster performance), whenusing an internal hollow cathode. Thruster performance and efficiencyhas been shown to increase by as much as 5% when using aninternally-mounted cathode compared to an external cathode. Internalcathode thruster configurations appear to minimize finite pressureeffects during ground tests, while thrusters using external cathodeshave shown non-flight-like coupling behaviors with the surroundingvacuum chamber (i.e. discharge current distributions). Furthermore, thehigh sensitivity of thruster performance to cathode positioning(directly related to thruster-cathode coupling) requires large rigidmounting brackets to precisely position a cathode. This requirementsignificantly increases the thruster's footprint, adds mass, increasesthe risk of damage during testing and spacecraft integration, andreduces the thruster's resistance to vibration loads, due to itsasymmetric geometry. Therefore, using an internal cathode, it ispossible to obviate the need for such brackets. In some embodiments, thecathode is therefore mounted internally and not externally in a bracket.

The person of ordinary skill in the art will understand that the Hallthrusters described in the present disclosure allow high efficiencyspacecraft to be launched for different space missions, having severaladvantages over more conventional ways for propulsion. For example,large chemical boosters can be utilized for SmallSat propulsion at theexpense of adding hundreds of kilograms to the launch mass of thespacecraft. However, an efficient, low power, long life Hall thrustercan fit within a SmallSat's mass and power budget, offering both thepropulsive capability to travel to deep space targets, as well assignificant maneuverability (such as second celestial body trajectory,plane-change, orbit raising, etc.) upon arrival. In addition,conventional spacecraft (mass ˜500-1,000 kg) traveling to Jupiter andbeyond using chemical and/or electric propulsion suffer from limitedmobility and orbit-insertion capabilities at their targets, due toeither the high propellant masses required for impulsive maneuvers orthe low solar power (<750 W) available at the target location.

A low power, high efficiency Hall thruster, however, can providemission-enabling maneuverability (orbit insertion, orbit and inclinationchanges, etc.) using <500 W of power. This power level is reasonablyattainable with solar power generator or a radioisotope thermoelectricgenerator. This propulsive capability at low power is currentlyunmatched by chemical systems of the same scale, especially given thesmall size and mass (including the required propellant) of modern SEPsystems.

To enable the development of a low-power, long-life, high-efficiency SEPsystem is enabled by the low-power magnetically shielded Hall thrusterdescribed in the present disclosure, as well as the ultra-compactlow-current hollow cathode that can be mounted internally to thelow-power Hall thruster. Magnetic shielding (MS) field topology has beenused in to both high and low-power Hall thrusters, however avoidingsaturation of the magnetic circuit in low-power magnetic shieldingdevices is considerably more challenging due to constraints on thethruster's size and power level. These constraints place sever limits onthe design and size of the center magnetic core, which has previouslyprohibited the use of a center-mounted cathode. Furthermore, maintaininghigh efficiency at low powers is a complicated optimization of thevarious design parameters of the thruster and been shown to lead tolower total efficiency in exchange for longer operational life.

The many advantages of MS shown by high power Hall thrusters, includingthe use of an on-axis center mounted cathode, would be beneficial to lowpower devices, however no flight-qualified low-power thrusters have beendeveloped using these technologies. Hollow cathodes used in flight Hallthrusters have traditionally been mounted externally to the thruster'smagnetic circuit, due to the lack of space on axis in the centermagnetic pole to accommodate an internally mounted cathode.

In fact, numerous Hall thrusters have shown a high degree of sensitivityto the placement of the external hollow cathode relative to the magneticfield topology. To compensate, large mounting brackets have beenimplemented in flight thrusters, to position conventionally sizedcathodes in exactly the right location. These brackets position thecathode externally to the thruster, and therefore significantly increasethe thruster's footprint. The brackets also add heavy fixturescantilevering the cathode, which can be easily bumped or damaged duringspacecraft integration. There are numerous advantages to having thehollow cathode on axis, but there is no available space in conventionalflight thrusters and there are no cathodes small enough to fit in thevery limited space available on axis on a <1 kW Hall thruster that canstill provide the required >10 kh life.

The solution to this problem is the development of a low power MS Hallthruster capable of accepting an internally-mounted ultra-compact hollowcathode. The low power thruster specification results in a low currentrequirement from the cathode, which allows very small cathodes to bedesigned and used. The thruster's magnetic circuit is specificallydesigned to avoid magnetic saturation while still providing sufficientspace for the cathode to be mounted along the centerline axis. Thecenter core design features a novel downstream counterbore where thecathode is inserted that maximizes the magnetic material available whileallowing enough space for the ultra-compact cathode. These features(optimized magnetic core shape and ultra-compact cathode geometry)combine to maintain the thruster's performance.

The MaSMi (Magnetically Shielded Miniature) Hall thruster program, whichpioneered the first low-power magnetically shielded Hall thruster in2012, has aimed to develop a low-power high efficiency Hall thrustercapable of Xe throughput higher than 100 kg. Several iterations of theMaSMi thruster have been developed, the most recent of which (theMaSMi-60) showed three key design features that limited the thruster'sperformance: An over-shielded magnetic field configuration, leading toincreased beam divergence; insufficient magnetic field strength, leadingto poor current utilization; and poor propellant flow distribution fromthe anode, leading to poor mass utilization.

During recent experiments, the MaSMi-60-LM2 demonstrated an 8% increasein total efficiency (10% increase in anode efficiency) through anoptimization of the magnetic circuit to address the overshielding andinsufficient magnetic field strength. The poor propellant flowdistribution will be addressed below in the present disclosure.

A version of a MaSMi thruster is termed MaSMi-DM, a magneticallyshielded low-power Hall thruster. The MaSMi-DM thruster builds on thedesign of the MaSMi-60-LM2 but incorporates several significantimprovements. The MaSMi-DM is designed to accept MaSMi's LUC (Lowcurrent Ultra compact Cathode), an internally-mounted low-currentultra-compact hollow cathode. At the core of MaSMi's LUC is a bariumoxide impregnated tungsten (BaO—W) cathode insert with an outer diameterof 4 mm, an inner diameter of 2 mm, and a length of 7.25 mm. The personof ordinary skill in the art will understand that in some embodimentsother dimensions may be used for the cathode insert or other parts ofthe thrusters of the present disclosure. In an effort to reduce futureproduction costs of MaSMi's LUC, the cathode tube was fabricated fromhigh-temperature stainless steel (a relatively unconventional materialfor this application) with an e-beam welded tantalum orifice plate. Inthis embodiment, the cathode tube was wrapped in a commerciallyavailable, 1.6 mm diameter, swaged tantalum heater, followed by 10layers of 0.025 mm thick tantalum foil as a radiation shield. Thegraphite keeper had an outer diameter of 13 mm.

MaSMi's LUC was designed for use in the long-life MaSMi-DM Hallthruster, therefore estimates of the cathode's insert life can becalculated using a barium depletion model. The cathode insert geometryand expected discharge current act as inputs to the model, which in thiscase are the dimensions stated above, and a value of 3 A for thecurrent—a reasonable upper-bound estimate of the discharge currentexpected from the MaSMi-DM. The current density (J) across the innersurface of the cathode insert is calculated from:

$\begin{matrix}{J = \frac{I_{D}}{\pi d_{i}L}} & (1)\end{matrix}$

where I_(d) is the discharge current, d_(i) is the cathode insert innerdiameter, and L is the cathode insert length. The maximum operatingtemperature (T_(max)) along the cathode insert is then approximatedusing a two-dimensional (2D) cathode temperature model. This model usesan assumed temperature drop across the insert, as well as its geometryand material, in an interpolation scheme to determine the inserttemperature required to generate the average current density found inEq. (1). The operating time to deplete the barium in the insert to adepth of 100 μm (τ_(100 μm)) can be calculated to be

$\begin{matrix}{{\ln \tau_{100\mu m}} = {{\frac{eV_{a}}{kT} + C_{1}} = {\frac{{2.8}482e}{kT} - {1{5.6}68}}}} & (2)\end{matrix}$

where e is the elementary charge, V_(a) is the activation energy, k isBoltzmann's constant, T is the temperature in Kelvin, and C₁ is a fitcoefficient. The cathode operating lifetime τ_(life) can then be derivedusing Eq. (2) together with the fact that the depletion depth isproportional to the square root of the operating time:

$\begin{matrix}{\tau_{life} = {\tau_{100\mu m}\left( \frac{y}{y_{ref}} \right)}^{2}} & (3)\end{matrix}$

where y is the insert thickness and y_(ref) is the barium depletionreference depth (in this case, 100 μm). Using Eqs. (1)-(3), the expectedoperational lifetime for the insert in the internal cathode (MaSMi'sLUC) exceeds 36 kh for a calculated T_(max) of 1233° C. and a 20%temperature drop across the cathode emitter length. The estimatedlifetime increases to more than 160 kh for an assumed temperature of1133° C., and decreases to 10 kh at 1333° C., both assuming the same 20%temperature drop across the insert.

The life of LaB₆ cathodes is determined primarily by evaporation of theinsert surface at the temperatures required for thermionic emission. Thethermionic emission current density (J) is given by theRichardson-Dushman equation:

J=AT ² exp(−eϕ/kT)  (1a)

where T is the surface temperature in Kelvin, e is the charge of anelectron, and k is the Boltzman constant. Lafferty determined that for aLaB₆ surface in vacuum, A=29 A/cm²K² and the work function ϕ=2.67 eV.Previously published lifetime models of the LaB₆ cathode have alwaysassumed a constant insert wall temperature due to the high thermalconductivity of LaB₆ and the use of a large cathode orifice diameterthat produces a flat density profile inside the insert and relativelyuniform heating. This uniform temperature assumption is supported bymeasurement of relatively flat axial plasma density profiles internal tothe cathode by an internal scanning probe over a large range in currentand cathode flow, suggesting relatively uniform heating. The life modelcalculated the temperature of the entire insert inner surface arearequired to produce the discharge current, and used that temperature tocalculate an evaporation rate using Lafferty's measured evaporation ratefor polycrystalline LaB₆ in vacuum. Lafferty has given an experimentallydeduced formula for the evaporation rate that fit his data:

$\begin{matrix}{W = \frac{10^{({C - {B/T}})}}{\sqrt{T}}} & \left( {2a} \right)\end{matrix}$

where W is the LaB₆ mass loss per unit surface area per time and B and Care constants, which according to Lafferty are B=36,850 K and C=13. Theprevious LaB₆ hollow cathode life model based on the Lafferty formula(Eq. 2a) adopted two conservative assumptions: the insert surfacetemperature is considered uniform along the entire area; and all theevaporated material is assumed to leave the insert region. The emissionsurface is then subjected to uniform evaporation and the insert innerdiameter, together with the effective emission area, increases withtime. Thus, the temperature required for emitting the same level ofdischarge current, calculated with the Richardson-Dushman equation (Eq.1a), decreases and, as a consequence, the evaporation rate reduces withtime. The insert lifetime ends when a pre-set minimum wall thickness isreached.

It should be noted that the emitter wall temperature of larger insertsthan used in MaSMi's LUC have been found to vary along the insertlength, as a function of the discharge current and cathode mass flowrates. The lifetime model can be revised to incorporate the measuredsurface temperature profile. The model discretizes the emitter into aseries of disks and uses the polynomial fit of the temperature profileto assign a temperature for each disk along the emitter length. Themodel then evaluates the emitted current density from each disk usingEq. 1a, and compares the integral of the current emitted along theentire insert with the discharge current. If the total emission currentdoes not match the discharge current, the code increases the polynomialfit of the temperature by adding a constant value until the emittedcurrent reaches the discharge current observed in the experiment. Thistechnique ignores the Schottky effect and back-flowing electron currentto the emitter surface, from the tail of the Maxwellian distributionovercoming the cathode-sheath. The Schottky term is found to be small,and ignoring back-flowing electron current is a good assumption forlow-pressure hollow cathodes because the sheath voltage is typically 3-5times the electron temperature and the backflow electron current issmall⁴³.

The model described above can be used to calculate the evaporation rateat each disk using Eq. 2a, and determines the mass loss along theemitter length for a preset time step. The model increments the time andre-evaluates the total emitter material loss, until the surface reachesa minimum defined thickness or all the material is evaporated todetermine the lifetime of the cathode. However, this complexity is notrequired for MaSMi's LUC because the LaB₆ emitter is short (<1 cm) andthe calculated internal density profile is relatively flat. Therefore,uniform insert temperature profiles are anticipated. The existing modelalso does not account for redeposition, which reduces the evaporationrate by over a factor of 2, and therefore gives a conservativeprediction of the lifetime of the insert.

Using the model described above, lifetime estimates as a function ofdischarge current can be calculated for MaSMi's LUC and illustrated asin FIG. 14. The end of the useful life of the LaB₆ emitter wasconsidered as occurring when the insert wall thickness reached 17% ofthe beginning-of-life (BOL) condition, representing the minimumstructural thickness of the insert. Assuming the emitter would only beused until twice its minimum structural thickness and recalling the lackof LaB₆ redeposition in the cathode life model, the useful life ofMaSMi's LUC (with a margin of at least 2×) is 10 kh, 18 kh, and 37 kh at5 A, 4 A, and 3 A of discharge current, respectively. These timescorrespond to a minimum total thruster propellant throughput of >200 kgXe (using the flow rates recorded during hot-fire testing).

A further improvement of the thrusters of the present disclosure can bedescribed with reference to the anode, which acts also as the gasdistributor. The anode was redesigned to allow for radial propellantinjection that reduces the axial velocity and achieves a highly uniformpropellant distribution, azimuthally around the discharge channel. Themagnetic circuit of the MaSMi-DM thruster was designed to replicate thetopology generated by the MaSMi-60-LM2 thruster, with a capability forabout 25% greater maximum radial field strength along the dischargechannel centerline (B_(r,max)), at approximately half the magnet power.Previously, a power of more than 70 W was required at the thruster'soperating temperatures. The goal of the new design was to improve totalthruster efficiency by reducing electrical power used for componentsthat do not directly contribute to thrust output (i.e. the magnetpower), while enabling a greater range of field settings to be tested.

Thruster plasma modeling was completed using Hall2De, a 2D axisymmetricsoftware code that allows for the simulation of the partially ionizedgas in the r-z plane of Hall thrusters. Ions are modeled as a cold(compared to electrons) isothermal fluid with charge exchange andmultiple ionization collisions accounted for in the momentum equationsas a friction (“drag”) force. For the neutral species, Hall2De assumesthat the particles incident on a surface are fully accommodated, andthat any re-emitted particles follow a cosine distribution. Therefore,the flux of neutrals on a given surface is a function of the view factorof that surface to all other surfaces, making the calculation of neutralparticle distributions primarily based on geometry. A mass-conservingfirst-order upwind algorithm is used to step the neutral gas particlesbetween grid cells, allowing the neutral density to change as a functionof time despite the particles having a fixed velocity (based on thevelocity distribution computed from the view factor particle fluxmodel). A 2D form of Ohm's law in directions parallel and perpendicularto the magnetic field and the electron energy equations are discretizedon a field-aligned computational mesh. The plasma potential isdetermined from Ohm's law combined with the current conservationequation. Experimentally-guided models of the anomalous collisionfrequency have enabled the results from Hall2De simulations to bevalidated against measured plasma parameters for numerous Hallthrusters. The primary features that distinguish Hall2De from other r-zplane plasma codes are a magnetic field aligned mesh (MFAM), nodiscrete-particle methods, and a large computational domain.

Plasma simulations of the MaSMi-DM were performed at a discharge voltage(V_(d)) of 300 V and a discharge power of 500 W. This voltage and powerwere held constant while the magnetic field was varied across a range ofmagnetic field strengths. At all modeled field strengths, thefundamental tenants of magnetic shielding (i.e. low electron temperatureand high plasma potential) were predicted as shown in the results forthe electron temperature (T_(e)) and plasma potential (ϕ) contourspresented in FIGS. 1-2. Peak predicted performance corresponded to athrust of 31.5 mN, an anode specific impulse of 1,590 s, and an anodeefficiency of 48% occurring concurrently. FIG. 1 illustratesHall2De-predicted electron temperature contours, while FIG. 2illustrates plasma potential contours for the MaSMi-DM operating at 300V and 500 W.

Erosion of the discharge channel walls (boron nitride, BN) and frontpole covers (purified graphite) was estimated to approximate thrusterlifetime. The peak erosion predicted on the discharge channel occurredalong the inner wall at the highest magnetic field settings, while thepeak pole cover erosion occurred on the inner pole cover at the lowestmagnetic field setting. At the nominal magnetic field setting, peakdischarge channel wall and pole cover erosion are predicted to be lessthan 5.3×10⁻³ mm/kh and less than 7.8×10⁻² mm/kh, respectively,indicating a thruster operational lifetime greater than 10 kh, based onthese erosion mechanisms and the thruster geometry.

Cathode characterization experiments were performed in a vacuum chambermeasuring 1 m in diameter by 2 m in length. A pair of cryogenic pumpsprovided a xenon pumping speed of approximately 2.5 kl/s. A single iongauge calibrated for xenon and mounted along the wall of the chamberprovided pressure measurements. The nitrogen base pressure of the systemwas less than 5×10⁻⁷ Torr. Operating pressures remained at less than8.2×10⁻⁵ Torr for characterization experiments (up to 0.29 mg/s Xe flowrate) and less than 9.1×10⁻⁴ Torr for heaterless ignition experiments(up to 3.9 mg/s Xe flow rate). Commercially available power supplies andpropellant flow controllers were used for all experiments. Researchgrade xenon was supplied to the cathode via electropolishedstainless-steel propellant lines.

MaSMi's LUC was mounted on a custom cathode bracket containing isolatedelectrical terminals for the cathode's heater and keeper leads. A 75 mmdiameter×100 mm long stainless steel hollow cylinder was used for ananode surface. The upstream opening of the anode was positioned 5 mmdownstream of the cathode keeper exit plane.

Anode propellant flow uniformity experiments were conducted in a 2.6 mdiameter by 5.2 m long cylindrical vacuum chamber. All internal surfacesof the chamber with line-of-sight to the thruster's discharge channelwere covered with either graphite panels or carbon felt. Three cryopumpsprovided a xenon pumping speed of approximately 40 kl/s. The chamberpressure was monitored by a wall-mounted ionization gauge calibrated forxenon. The nitrogen base pressure of the system was less than 1×10⁻⁷Torr, and during operation with xenon flow of up to 3.0 mg/s, thechamber pressure remained less than 1×10⁻⁵ Torr. Commercially availablepower supplies and propellant flow controllers were used for allexperiments. Research-grade xenon was supplied to the thruster viaelectropolished stainless steel propellant lines.

To ensure the uniform distribution of neutral gas within the dischargechannel, a series of flow tests were performed under vacuum using pitottubes. This approach mirrors similar approaches used in the past toverify anode flow uniformity for Hall thruster propellant manifolds. Thestandard success criteria for flow (or pressure) uniformity used toaccept a thruster anode manifold is ≤5% variation from the mean flow.Both the anode manifold and the discharge channel walls are included toensure the flow is as representative as possible during thrusteroperation. Due to the small dimensions of the MaSMi-DM dischargechannel, a ⅛″ stainless steel tube with an inner diameter of 1.39 mmserved as the pitot probe. This tube size was selected to obtainsufficient spatial resolution while minimizing perturbations of the flowenvironment. Based on previous pressure variation measurements, thepitot probe inlet was fixed radially along the channel centerline (b/2)and axially at the channel midpoint (L/2). A rotational stage was usedto rotate the discharge channel and anode relative to the pitot probe,enabling the positioning of the pitot probe tip at a total of 36equally-spaced azimuthal locations with ±0.0125° resolution.

Thruster performance testing was conducted in a vacuum facility asdescribed above. For these tests, the chamber pressure was monitored bytwo ionization gauges calibrated for xenon. The first gauge used anS-shaped snorkel inlet and was positioned in the thruster exit planeapproximately 60 cm radially from the thruster axis (the midpointbetween the thruster and chamber wall); this was used as the primaryindication of chamber pressure. The second gauge was mounted along thechamber wall just downstream of the thruster exit plane. Both ion gaugeshave a plasma screen (i.e. metallic mesh) at their respective inlets.

A water-cooled inclination-controlled inverted-pendulum thrust stand wasused to measure the thrust of the MaSMi-DM. The thrust stand wascalibrated by lowering and raising a series of precision masses. Thecalibration was performed before and after each experimental run, withthrust stand zeros performed after each thrust measurement. The thruststand demonstrated a resolution of 0.1 mN with an estimated uncertaintyof 2.0%. Combined with the other thruster system uncertainties (powersupplies, flow controllers, etc.), the estimated uncertainty in theI_(sp) and efficiency were 2.2% and 4.2%, respectively.

Three Type-K thermocouples were installed on the thruster to monitortemperature. The first was located on the upstream face of thethruster's back pole. The second was mounted on the outer diameter ofthe front outer pole, just upstream of the graphite pole cover. Thethird was embedded in the inner magnet coil. An additional 6 Type-Kthermocouples were mounted throughout the thrust stand to monitor thethermal stability of the diagnostic.

The diagnostics rig to test the plasma is a removable structure thatincludes a flat Langmuir probe, an E×B probe, and a retarding potentialanalyzer. A shielded Faraday probe is mounted on a rotation stagecentered at the thruster exit plane along the thruster's centerlineaxis. All thruster-facing surfaces of the probes and mounting hardware(with the exception of the probe measurement regions) were covered ingraphite shielding. Measurement of the plasma discharge current andvoltage oscillations were performed using broadband transducers coupledto a 12-bit 8-channel oscilloscope set to a 100 MHz sample rate. Thecurrent was measured on the anode side of the discharge supply with aPearson 110 coil, providing upper frequency response of 20 MHz, and onthe cathode side of the discharge supply with a shunt read into adigital multimeter to capture the DC response. The discharge (i.e.anode-to-cathode) and cathode-to-ground voltages were measured withseparate active high-voltage differential probes.

To characterize the performance of MaSMi's LUC, two sets of experimentswere conducted. The first involved mapping the discharge-currentbehavior of the cathode across a range of propellant flow rates. Normalheating of the cathode, using its swaged heater to achieve ignition, wasused for these tests. The second set of experiments demonstrated theheaterless ignition capabilities of MaSMi's LUC.

Cathode experiments to characterize the discharge current-voltagebehavior began with the same cathode ignition process followingconditioning of the BaO—W insert. The heater was supplied with 5.5 A ofcurrent, providing less than 28 W of heater power, for 6 minutes. Duringthe heating process, a 0.20 mg/s xenon flow rate was established in thecathode. The application of a 150 V keeper voltage (V_(k)) with a 2 Acurrent limit consistently ignited MaSMi's LUC. With a 2 A keeperdischarge established, the flow rate was altered for the desiredcondition. The discharge was then connected to the anode at the desireddischarge current, followed by removal of the keeper current. Thedischarge current was then incrementally increased from the loweststable condition to the highest while the discharge voltage wasrecorded. A dwell time of ≥5 minute at each condition was performedprior to taking data to allow the discharge to settle. Due to the addedsputter erosion of the cathode, and potentially also of other thrustercomponents, at high cathode discharge voltages (corresponding to largecathode-to-ground voltages during thruster operation), no data wascollected for flow and current combinations yielding V_(d)>35 V.

The discharge voltage behavior of MaSMi's LUC as a function of dischargecurrent and propellant flow rate was mapped to assess the compatibilityof the compact cathode with the MaSMi-DM thruster. Flow rates were setfrom 0.10-0.30 mg/s in increments of 0.05 mg/s while the dischargecurrent was varied from 0.2-4 A in increments of 0.1 A from 0.2-0.5 Aand increments of 0.25 A from 0.5-4 A. Results are presented in FIG. 3where conditions that did not yield a stable discharge are not reported.MaSMi's LUC demonstrated stable operation over the full range ofexpected thruster discharge currents. Discharge voltages remained flatfrom 0.5-4 A for all but the 0.10 mg/s flow rate, varying by <5 V in theworst case. This behavior suggests both an appropriate orifice sizingfor the application as well as a strong thermal design (i.e. maintainingthermal isolation of the insert with minimal heat losses due toconduction and radiation).

A key single-point failure of a conventional hollow cathode is theheater, leading to the consideration of heaterless cathodes. Heaterlesscathode ignition is known to the person of ordinary skill in the art.Heaterless cathode ignition consists of an electrical breakdown processbetween the keeper and cathode orifice or insert, leading to heating ofthe insert. Past experiments have revealed several unique potentialfailure mechanisms related to repeated heaterless ignitions, includingbarium depletion of the insert, arc breakdown damage of the cathode tubeand orifice plate during ignition, and sustained arc damage duringcathode heating. However, experimental testing has shown eitherinconclusive or minimal risk to cathode lifetime due to hundreds orthousands of heaterless ignitions. To demonstrate operation of MaSMi'sLUC in the event of a heater failure, and to characterize the ignitionbehavior in preparation for possible future iterations of the cathode, aseries of heaterless ignition trials were performed.

Heaterless ignition of MaSMi's LUC was achieved by supplying highpropellant flow rates (˜10× the rates required for normal operation) andsweeping V_(k) from 0-1,500 V until a Paschen breakdown occurred.Because heaterless cathode ignition is a destructive process, the keepercurrent was limited to 150 mA in all trials but two (limited to 300 mA),to reduce orifice plate damage through a reduction in the power of thefield emission between the keeper and orifice plate, while alsopreventing sufficient current between the two electrodes that wouldenable an explosive vacuum arc. The keeper-orifice plate field emissionwas allowed to heat the cathode until the insert reached thermionicemission temperatures, identified by a significant drop in the keepervoltage corresponding to facilitated electron emission by the lowwork-function emitter. Each ignition trial ended with the application ofa 2 A discharge current to the downstream anode, followed by immediateremoval of the keeper current and reduction of propellant flow to 0.20mg/s to demonstrate normal cathode operation. A 1 kΩ resistor and a 180pH inductor were installed in series with the positive side of thekeeper supply to filter voltage spikes and limit the peak current duringthe ignition process.

Heaterless ignitions trials were performed with propellant flow rates of2.0-3.9 mg/s in increments of 0.98 mg/s with a total of 10 ignitions ateach flow rate. Each ignition was separated by 5 minutes to enable theinsert to cool below thermionic ignition temperatures and each set of 10ignitions was separated by ≥90 minutes to allow the cathode to cool to a“cold” condition.

The keeper voltage at which the field emission was established betweenthe keeper and orifice plate was recorded and is illustrated in FIG. 4.Each data point (405) in FIG. 4 represents the average of the 10ignitions at the given flow rate. As expected, the average ignitionvoltage followed a trend characterized by a power law (via Paschen'sLaw). This trend line (410) is plotted in FIG. 4 along with its equation(415) and coefficient of determination or R² value (420). The error bars(425) represent the span of keeper voltages required to establish fieldemission, demonstrating the changes to, and variability in, surfacemorphology of the orifice plate due to repeated heaterless ignitionprocesses.

The time for cathode ignition was recorded for the first of each set of10 ignitions, representing the time to ignite the cathode from a coldcondition. The keeper voltage immediately after ignition ranged from140-310 V. For a keeper current of 150 mA, this corresponded to 21-47 Wof power was incident on the cathode orifice plate upon initiation offield emission. This power steadily decayed until the insert reachedthermionic emission temperatures, at which point V_(k) dropped tobetween 31-95 V corresponding to an incident power of 5-14 W. Theaverage heating time (i.e. time until cathode ignition afterestablishing field emission) was 82 s with a maximum time of 120 s (3.4mg/s) and a minimum time of 55 s (2.9 mg/s). For comparison, ignitionsfrom a cold condition at a keeper current of 300 mA were performed at2.5 mg/s and 3.4 mg/s resulting in identical ignition times of 56 s.While the risk of vacuum arcs is greater at 300 mA than at 150 mA, theadditional power transferred into the cathode via field emission netteda 26 s (32%) reduction in ignition time.

Anode propellant flow uniformity experiments were also conducted. Priorto measuring the MaSMi-DM's anode manifold flow uniformity, the flowresponse of the pitot probe was characterized. The relatively smallpitot tube orifice and long tubing lengths limit the gas conductance tothe pressure sensing filaments inside the ion gauge. An estimate of thetime to affect a given change in pressure (tap) is obtained withstandard vacuum conductances:

$\begin{matrix}{t_{\Delta P} = {\frac{V_{gauge}}{S_{eff}}{\log \left( \frac{P_{o} + {\Delta P}}{P_{o}} \right)}}} & (4)\end{matrix}$

where V_(gauge) is the internal volume of the ion gauge (including thepitot tube assembly), S_(eff) is the effective conductance, d is thepitot tube inner diameter, L is the overall pitot tube length, and P_(o)is the reference pressure. The internal volume of the ion gauge isestimated as 0.25 liter, and molecular flow is assumed due to Knudsennumbers of 10 to 100 for the pressure range 10⁻³-10⁻² Torr. Applyingknown quantities to Eq. (4) to find the time to observe a 10% change inpressure (t_(10%ΔP)) yields:

$\begin{matrix}{{t_{10\% \Delta P} \approx {\frac{V_{gauge}}{\begin{pmatrix}{121 \cdot} \\{d^{3}\text{/}L}\end{pmatrix}}{\log\left( \frac{\begin{matrix}{P_{o} +} \\{\Delta \; P}\end{matrix}}{P_{o}} \right)}}} = {{\frac{\begin{matrix}{0.25 \times} \\{10^{- 3}m^{3}}\end{matrix}}{\begin{matrix}{121 \cdot} \\\begin{matrix}{\left( {1.4 \times 10^{- 3}m} \right)^{3}/} \\{0.19\mspace{14mu} m}\end{matrix}\end{matrix}}{\log \left( {1.1} \right)}} = {6\mspace{14mu} s}}} & (5)\end{matrix}$

The calculated settling time of 6 s was experimentally validated througha pressure versus time measurement, the results of which are illustratedin FIG. 5. The measured flow response also includes the time response ofthe flow through the propellant lines from the vacuum chamber wall tothe anode manifold. Regardless, a 10% drop in local pressure inside thedischarge channel was observed to occur within 13 s (larger due to thefinite length propellant lines), thereby validating the estimate of 6 s.To guarantee accurate pressure measurements for this test, a 20 ssettling time was used between consecutive measurements.

The propellant flow uniformity for MaSMi-DM's anode was measured at 1mg/s and 3 mg/s to approximately capture a “low-flow” and a “high-flow”condition. To ensure repeatability with the flow uniformity measurement,each azimuthal location was measured twice per flow rate (rotating themanifold ±360°). The results for the two flow conditions are illustratedin FIG. 6, where datapoints (605) are for a propellant flow rate of 3mg/s, and datapoints (610) are for a rate of 1 mg/s. The flow uniformitydemonstrated by the MaSMi-DM anode is well within the ≤10% variationrequirement. Total peak-to-peak non-uniformity was 3.2% at 1 mg/s and2.6% at 3 mg/s. The maximum non-uniformity, which was observed at thelower 1 mg/sec flow rate, was only 1.6% below the mean value. Based onthese results, the MaSMi-DM anode flow uniformity is well below thatmeasured in other high efficiency Hall thrusters.

Thruster performance was also tested. In particular, testing of theMaSMi-DM has consisted of three hot-fire sessions totaling less than 10h of operation time and including a bake-out procedure and initialperformance mapping. During all thruster firings, the magnetic field wasset to what was judged to be near the nominal setting; future testingwill confirm or modify this value. The thruster was operated in acathode-tied electrical configuration i.e. the thruster body waselectrically tied to cathode common. The cathode, in this experiment,was operated without any applied keeper current and with a cathode flowfraction (defined as the cathode flow rate divided by the anode flowrate, {dot over (m)}_(c)/{dot over (m)}_(a)) of between 2-7%.

Thruster bake-out was performed at a discharge voltage of 300 V whilethe power was slowly increased from ˜300 W to ˜550 W in steps of ˜50 Wuntil thermal steady state was approached. At each step, the dischargepower was observed to rise (heating-related outgassing), fall (reducedoutgassing), and then stabilize before advancing to the next powerlevel. The thruster was assumed to approach thermal steady state whenthe thruster temperatures were changing by ≤10° C./h and the dischargecurrent at a given discharge voltage and flow rate varied by ≤±0.025A/h. The maximum temperatures observed that met the aforementionednear-steady state conditions were 286° C., 233° C., and 337° C. on theback pole, front outer pole, and inner coil, respectively. Reachingthese temperatures took <3 h from the thruster's initial temperature of˜15° C. No performance data was recorded during the bake-out.

During the early stages of performance mapping, several failuresoccurred in the ground support equipment (GSE) for the vacuum facilitywhich prevented a thorough characterization of the thruster. However,some noteworthy data were recorded during the initial hours of thrusteroperation. Prior to the GSE failure and with the discharge voltagemaintained at 300 V, the discharge power (Pd) was varied from 300-550 Wat the assumed nominal magnetic field setting. Peak performance wasmeasured at 500 W with a thrust (T) of 34.3 mN, an anode efficiency(η_(a)) of 45%, a total efficiency (η_(t)) of 41%, and an anode andtotal specific impulse (I_(sp,a), I_(sp,t)) of 1370 s and 1320 s,respectively, according to the following equations:

$\begin{matrix}{\eta_{a} = {{\frac{T^{2}}{2{\overset{.}{m}}_{a}P_{d}}\mspace{14mu} \eta_{t}} = \frac{T^{2}}{2{\overset{.}{m}}_{t}P_{t}}}} & (6) \\{I_{{sp},a} = {{\frac{T}{{\overset{.}{m}}_{a}g}\mspace{14mu} I_{{sp},t}} = \frac{T}{{\overset{.}{m}}_{t}g}}} & (7)\end{matrix}$

where {dot over (m)}_(a) is the anode propellant mass flow rate, {dotover (m)}_(t) is the total propellant mass flow rate, P_(t) is the totalthruster power (discharge, keeper, magnet, etc.), and g is Earth'sgravitational acceleration. Several other operating points resulted intotal efficiencies of ˜40% (anode efficiencies>42%) and specificimpulses of >1,400 s. These performance data, which were taken atnon-optimized thruster operating points for the MaSMi-DM, show goodagreement with the performance predicted by Hall2De as presented in thepresent disclosure. Furthermore, they indicate a ≥25% increase in totaland anode efficiency compared with the previous generation MaSMi-60-LM2which demonstrated 32% total efficiency and 39% anode efficiency.

During further testing, the thruster accrued 100.1 h of operating timeand processed 0.92 kg Xe. MaSMi's LUC demonstrated 102 heaterlessignitions with no observable changes to ignition time, stability, etc.The MaSMi-DM was operated over a discharge voltage range of 200-600 V inincrements of 100 V, a discharge current range of 0.5-4 A in incrementsof 0.5 A, and a discharge power range of 150-1000 W. At dischargevoltages beyond 400 V, the minimum discharge current was increased to 1A. A summary plot of the operating points examined is presented in FIG.15. At each current-voltage (I-V) condition, the magnetic field (B) wasswept from the minimum to the maximum setting, spanning ±40% from themedian setting, to identify the peak performance point (i.e. highesttotal efficiency) as well as any unfavorable operating regimes. Testingwas performed at constant discharge current; as such, the propellantflow rate was adjusted as necessary as the magnetic field setting waschanged. The results presented in the following sections are based onthe performance recorded at the peak performance point of each I-V-Btrace.

Thrust at each discharge voltage as a function of discharge power isillustrated in FIG. 16. The thrust curves are highly linear withincreases the discharge power yielding proportional increases in thrust.A peak thrust of 62.7 mN at 200 V and 800 W was recorded, which waslimited by the discharge current limits set for the campaign; thrustsof >70 mN at 200 V & 1000 W appear possible should that condition beadvantageous in future mission planning. A slight deviation fromlinearity was observed in the 200 V thrust curve at 300 W, where themeasured thrust dipped slightly (note that this behavior is consistentwith the MaSMi-60-LM1)²⁵. This was a repeatable behavior not observed atother power conditions. FIG. 16 illustrates data for 200 V (1605), 300 V(1610), 400 V (1615), 500 V (1620), and 600 V (1625).

Total specific impulse at each discharge voltage as a function ofdischarge power is illustrated in FIG. 24. Higher discharge voltagesyielded higher I_(sp) once a sufficiently high current density wasachieved, which corresponded to between 1-1.5 A of discharge current. Apeak I_(sp) of 1940 s was recorded at 500 V and 1000 W, and 1500 s wasachievable at multiple discharge voltages beyond 500 W. FIG. 24illustrates data for 200 V (2405), 300 V (2410), 400 V (2415), 500 V(2420), and 600 V (2425).

Total thrust efficiency at each discharge voltage as a function ofdischarge power is presented in FIG. 25. Thruster efficiency steadilyincreased with discharge current (tied to current density) until ˜1.5 Awhere each curve began to plateau. The MaSMi-DM demonstrated a peaktotal efficiency of 53% with efficiencies of ≥40% available as low as˜300 W. It can be noted that the Hall2De thrust, anode I_(sp), and anodeefficiency predictions of 31.5 mN, 1590 s, and 48% at 300 V and 500 Wmatched well with the measured values of 33.9 mN, 1500 s, and 50%(determined by linear interpolation between the 450 W and 600 W cases at300 V). FIG. 25 illustrates data for 200 V (2505), 300 V (2510), 400 V(2515), 500 V (2520), and 600 V (2525).

A summary of the discharge current oscillations, presented as a ratio ofthe peak-to-peak discharge current oscillations (I_(d,p2p)) to the meandischarge current (I_(d,mean)) at each discharge voltage, as a functionof discharge current is shown in FIG. 26. In every case, peak-to-peakoscillations dropped to ≤100% of the mean current beyond 1.5 A oddischarge current. Oscillations remained ≤150% of the mean current forall conditions except for four, occurring at 300 V and 400 V and ≤1 A ofdischarge current. FIG. 26 illustrates data for 200 V (2605), 300 V(2610), 400 V (2615), 500 V (2620), and 600 V (2625).

Analysis of the plasma near the discharge channel revealed magneticshielding in the thruster. Dark zones were observed between the highdensity plasma, near the thruster exit plane, and the discharge channelsurfaces. These dark zones are associated with low local electrontemperatures near the channel walls. The low electron temperatures alongthe channel walls, corresponding to low local xenon excitation ratesnear the channel surfaces, is a visual indication of a magneticallyshielding Hall thruster field topology. Furthermore, the dischargechannel, after the thruster's operation, was found coated in a layer ofback-sputtered graphite free of any white zones (BN cleaned of carbonback-sputter by xenon ion-bombardment). Blackened channel walls are anecessary feature, but not a sufficient condition, for magneticshielding to exist. Previous MaSMi testing measured carbon backsputterrates of 0.03-0.06 μm/h at a discharge voltage of 300 V, correspondingto discharge channel erosion rates of 0.06-1.13 μm/h. However, higherbacksputter rates were expected due to the proximity of the plasmadiagnostics rig. Nevertheless, the combination of Hall2De plasmasimulations (constant predicted plasma potential along the channel, lowpredicted wall electron temperature, and low predicted erosion), darkzones local to the channel walls during thruster operation, andcarbon-coated channel walls after operation indicates that the MaSMi-DMgenerates a fully shielding magnetic field topology.

Typical high speed telemetry collected during operation of the MaSMi-DMare illustrated in FIG. 8, where both the time series and power spectraldensity (PSD) data are presented for the thruster operating at 300 V and500 W. Scope data were collected for 0.5 seconds at each condition toprovide sufficient statistical accuracy for the various unsteady andturbulent plasma modes. The anode current generally showed breathingmode oscillations with frequencies between 20-50 kHz. Over the 0.5 ssample interval, the peak-to-peak was consistently on the order of50-300% of the mean current while the standard deviation remained <10%of the mean current at most of the operation points. It should be notedthat the values in the legend of FIG. 8 are based on the full 0.5-sdataset and therefore hold statistical significance. The dischargevoltage showed up to <2% voltage spikes that were correlated to theturbulent breathing mode oscillations. The cathode-to-ground voltagefollowed the anode potential and discharge current oscillations with apeak-to-peak voltage of ˜0.6 V. The PSDs of these three signals clearlyshow the Hall thruster breathing mode centered at 28 kHz (otherconditions showed stronger and more coherent breathing modeoscillations). Several higher frequency features at 87 kHz and at 1.3MHz were also observed that may include cathode modes based on priorstudies with magnetically shielded Hall thrusters. While this conditionshows the 1.3 MHz mode in all three signals (anode current,anode-to-cathode voltage, and cathode-to-ground voltage), otherconditions (not shown) retain this 1.3 MHz mode only in the cathodesignals. Since anode current oscillations were not observed at 87 kHzand appeared at 1.3 MHz only at certain operation conditions, these twofeatures could be cathode specific or azimuthally rotating spokes.

A development model version of the low-power magnetically shielded MaSMiHall thruster with an internally-mounted low-current ultra-compacthollow cathode (MaSMi's LUC) was designed, fabricated, and subjected tocomponent and initial performance testing. In addition to the novelinternally-mounted hollow cathode, the MaSMi-DM incorporates an improvedgas distributor and magnet coil design, yielding uniform propellant flowthrough the discharge channel and low required magnet powers,respectively. A barium-depletion life model for MaSMi's LUC designsuggested an operational lifetime of >36 kh, which provides marginagainst the thruster lifetime goal of >10 kh. Plasma simulations of theMaSMi-DM predicted strong performance, with near 50% anode efficienciesand near 1,600 s specific impulse at 500 W of discharge power.

Independent characterization testing of the cathode revealed flatdischarge voltage versus discharge current behavior across the range ofexpected operating flow rates and thruster discharge currents.Furthermore, a series of heaterless cathode ignition trials wereperformed to demonstrate the capability and to provide an initialindication of the system requirements to ignite MaSMi's LUC in the eventof a cathode heater failure. While integrated cathode/thruster testingwas limited by facility failures, several performance data points wererecorded at non-optimized thruster operating conditions. Totalefficiencies of ˜40% (anode efficiencies of >42%) and specific impulsesof >1,400 s were calculated from thrust measurements, with a peak totalefficiency of 41% corresponding to a peak anode efficiency of 45%. Thisrepresents a ≥25% performance improvement over the previous generationMaSMi-60-LM2 and indicates that further increases in performance arepossible after optimizing the thruster operating points.

A cross-section, in perspect view, of the low-power MS Hall thruster andultra-compact low-current hollow cathode described in the presentdisclosure is illustrated in FIG. 9. The key design features that enablethis technology's implementation are the thruster's inner core design,which has sufficient magnetic material along the thruster axis tosupport the magnetic flux necessary to produce a distortion-free MSfield topology, as well as the axially-short ultra-compact cathode,which enables internal mounting while reducing the geometric impact onthe thruster's magnetic circuit. In some embodiments, the axial lengthof the thruster in FIG. 9 is about 10 cm. FIG. 9 illustrates theMaSMi-DM low-power Hall thruster with a heater-based ultra-compactlow-current hollow cathode mounted internally and along the thruster'scenterline. FIG. 9 illustrates an exemplary cross-section of a Hallthruster with the internally mounted hollow cathode and dischargechannel highlighted. A more detailed outline of the thruster isillustrated in the following figures. In FIG. 9, the thruster'scenterline axis (905) is illustrated. The thruster has azimuthalsymmetry around this axis, as can be understood from FIG. 9. FIG. 9illustrates the hollow cathode (910). In some embodiments, a coil heateras described below is placed at the location of hollow cathode. Acathode propellant tube can be placed along the centerline axis, takingadvantage of the hollow volume in the center of the thruster. FIG. 9illustrates the magnetic circuit (915), the outer magnet coil (920), theinner magnet coil (925), and the anode (930); all these elements, aswell as the cathode, have azimuthal symmetry around the centerline axis.

Traditionally, flight and flight-like hollow cathodes have used acontinuous diameter along their full axial length to facilitatefabrication and provide sufficient thermal isolation from the mountingflange on the back of the thruster. In higher-power thrusters using aninternally-mounted cathode, the entire cathode assembly is mounted alongthe thruster centerline requiring a large center bore to be made alongthe centerline of the thruster's inner core. This moves the thruster'smagnetic circuit components radially outward, to maintain sufficientmagnetic material along the thruster's inner core to avoid saturation, acondition which can distort the magnetic field topology and compromisethe thruster's operation and performance. As a result of the largediameter components with an internally-mounted cathode, the thruster isdriven to a higher nominal power.

The thruster described in the present disclosure uses an inner core withan axially varying diameter. The upstream section is the larger indiameter to support high magnetic flux and force any saturation effectsfurther downstream, thereby giving the maximum cross-channel fieldstrength possible. The ultra-compact cathode design, illustrated in FIG.10, only requires a larger bore near the downstream end of thethruster's inner core, as seen in FIG. 9 (915), FIG. 10 (1005), and FIG.11 (1105). Therefore, the remaining part of the inner core can be boredwith a smaller diameter (1110) to accommodate the cathode propellantdelivery line. Unlike conventional internally-mounted cathodes, thepropellant and electrical lines of the ultra-compact cathode can berouted along and/or parallel to the thruster axis using small diameterholes (1115) along the thruster length. This enables the cross-sectionalarea of the center core to be maximized in the space available, giventhe constraints of the remaining thruster geometry, thereby preventingsignificant impact to the thruster's magnetic circuit and minimizing thediameter of the thruster's discharge channel (i.e. minimizing thenominal operating power).

Additionally, the cathode tube is designed to be only as long as thebarium oxide-impregnated tungsten (BaO—W) or lanthanum-hexaboride (LaB₆)thermionic electron emitter, with the outer diameter of the cathode tubedetermined by the lifetime requirement of the emitter. The baselinedesign shown in FIG. 11 is capable of >10 kh. Because a short axiallength is a driving feature of the new cathode design, only the portionof the cathode tube housing the emitter is larger in diameter than thepropellant line. This allows the cathode tube to accept a larger volumeemitter (i.e. longer life) in a shorter axial distance, compared toconventional designs that use the same diameter tube for both thecathode tube and propellant line.

Sufficient thermal isolation of the cathode, providing an efficientplasma discharge with low power losses from the electron emitter, wasachieved by thinning the walls of specific areas of the cathode tube andpropellant line to create thermal chokes. By reducing thecross-sectional area of the cathode tube and propellant lineperpendicular to the direction of heat flow, the ability of the tube tothermally conduct heat away from the thermionic insert is minimized.FIG. 10 illustrates different views of an ultra-compact low-currenthollow cathode with a swaged coil heater. Some electrical connectionsare also illustrated (1015, 1010). The position of the coil heaterwithin the thruster is illustrated also in FIG. 11 (1120).

Two cathode heating and ignition technologies can be applied within thesmall dimensions of the ultra-compact cathode: high voltage breakdownand swaged coil resistive heaters. High voltage breakdown-type cathodes,also known as “heaterless” cathodes, use a Paschen breakdown mechanism,between the cathode orifice plate and the external keeper electrode, tostrike the cathode discharge. The Paschen breakdown mechanism comprisesa low current electrical arc traveling through a gaseous medium withhigh local pressure. These cathodes have very small form factors due tothe lack of a dedicated electrical heater, but have a slightly morecomplicated start-up procedure compared to other cathodes. Lifetimes ofheaterless cathodes using a tungsten orifice plate over the thermionicemitter have been shown to be of the same order as those of cathodesusing heaters, with tens of thousands of starts demonstrated inlaboratory environments.

Alternative cathodes are swaged coil heater cathodes, which use aresistive heating element coiled around the cathode tube (as illustratedin FIG. 10) to heat the thermionic emitter to the ignition threshold,and allow striking of the discharge. The number of cathode startspossible with coil heaters is determined by the robustness of theheater. Swaged heaters have demonstrated thousands of starts andcontinuous operating times greater than 10 kh.

Both heater-based and heaterless ultra-compact low-current cathodes havebeen demonstrated with the MaSMi-DM thruster. Both high voltagebreakdown and swaged coil heater cathode designs provide a long-life,multi-start operation. To date, Hall thrusters using aninternally-mounted cathode operate at high-power (>1.5 kW) using axiallylong, large-diameter cathodes. To date, no Hall thruster with aninternally mounted cathode has been flown. The Hall thruster magneticcircuit design of the present disclosure can accommodate anultra-compact low-current cathode and is an innovative architecture thatenables the improvements to performance, operational stability, and ionbeam symmetry demonstrated by high power thrusters using internallymounted cathodes.

With regard to thermal choking, discussed above with reference tothermal conduction within the thruster, it is known to the person ofordinary skill in the art that cathodes use thermionic emitters, whichmust be raised to a specific threshold temperature (material dependent)to emit electrons and allow the cathode to function. Ideal steady-stateoperation of a cathode requires no external sources of power to add heatto the emitter and maintain a cathode discharge. Resistive heatingcaused by the electron-rich plasma exiting the cathode orifice issufficient to keep the emitter hot enough for stable operation; this isknown as cathode self-heating. If the emitter becomes too cold tomaintain the cathode discharge (e.g. the discharge is not drawingsufficient current to maintain cathode self-heating), the cathodedischarge will become unstable and eventually extinguish. An electriccurrent may be drawn to the cathode keeper to enable operation atlower-than-nominal discharge currents (i.e. effectively pulling extracurrent through the cathode to the keeper and thereby elevating thecathode emitter temperature). However, this process comes at the expenseof electrical efficiency; power is being used for the keeper and notdirectly contributing to the production of thrust.

To enable cathode operation at low discharge currents, cathode designfeatures must be implemented to keep the thermionic emitter hot enoughfor electron production. One key method is attaining a high level ofthermal isolation of the cathode emitter by use of low thermalconduction materials in the cathode. By preventing conductive heattransfer upstream along the cathode tube, the cathode emitter maintainshigher temperatures at lower discharge currents.

Magnetic shielding is a unique field topology achieved through carefuldesign of the thruster's magnetic circuit. Magnetic hollow cylinders,called “screens”, are located radially inward and outward of thedischarge channel walls. These screens are magnetically coupled to thethruster's magnetic circuit and are important for producing a MS fieldtopology. As these screens are extended towards the exit plane, asignificant fraction of the magnetic flux emanating from the polepieces, and crossing the discharge channel gap, is shunted through thescreens, forcing the local curvature of the magnetic field. This localcurvature causes the field lines, that leave one pole piece and crossthe channel gap, to turn upstream, towards the anode, before turningdownstream and reconnecting to the opposite pole piece. A more detailedexplanation of the unique features of an MS field topology and theplasma physics describing the benefits to thruster lifetime andperformance is known to the person of ordinary skill in the art, withcertain features described in U.S. Pat. No. 9,453,502, the disclosure ofwhich is incorporated herein by reference in its entirety.

Two geometric configurations of these screens have been used to design aMS Hall thruster magnetic circuit to date. The first configurationconfigures the cylinders as a magnetic shunt, which is a one-pieceannular component with a U-shaped cross-section that surrounds thedischarge channel. Originally implemented in Hall thrusters to improvebeam focusing (i.e. lensing) through the introduction of a small amountof magnetic field curvature across the channel gap, the shunt ismagnetically coupled to the thruster's magnetic circuit but does notphysically connect to the other magnetic circuit components. Across-section of one variant of such a Hall thruster, incorporating amagnetic shunt, is illustrated in FIG. 12. The magnetic shunt (1205) isillustrated in FIG. 12 in a cross section view. The magnetic shunt hasazimuthal symmetry as can be understood from FIG. 12. The person ofordinary skill in the art will understand that Hall thrusters aregenerally illustrated as in FIG. 11 and FIG. 12, where the longitudinaldirection of the thruster is in the plane of the figure, while theradial direction is perpendicular to the longitudinal axis, and theazimuthal direction is along a circumference in a plane including theradial directions, and normal to the longitudinal axis. Therefore, Hallthrusters in such cross section views generally have azimuthal symmetrywith regard to several components, such as the magnetic shields and thecathode emitter.

The benefits of a magnetic shunt are its lower mass and reducedgeometric interference with the thruster's internal components upstreamof the discharge channel. However, because the shunt is not physicallytied to the back pole, a shunt is not able to support large amounts ofmagnetic flux before saturating. Thrusters using magnetic shuntstherefore tend to produce weaker MS field topologies, making itchallenging to produce an optimal degree of curvature near thedownstream edges of the discharge channel, to obtain a full magneticshielding configuration. In addition, magnetic shunts are largelythermally isolated, which can cause problems with thermal-inducedchanges to their magnetic properties.

The second geometric configuration uses screens configured as a pair ofconcentric, hollow, cylindrical components located radially inward andoutward from the discharge channel walls. The cylindrical components arephysically connected to the thruster's back pole. This physicalconnection yields much stronger magnetic coupling to the thruster'smagnetic circuit, and provides a strong thermal conduction path to thethruster's radiating surfaces, to control the temperature of thescreens. Therefore, magnetic screens using this second geometricconfiguration are far less susceptible to magnetic saturation comparedto shunts, and are able to generate stronger levels of magneticshielding (i.e. a higher curvature in the magnetic field). Across-section of a variant of a Hall thruster using magnetic screens isillustrated in FIG. 13. In FIG. 13, the magnetic screens (1305) areillustrated.

The difference described above between the first geometric configurationand the second geometric configuration can be noted by comparing FIG. 12and FIG. 13. In FIG. 13, the screens (1305) are in physical contact tothe back pole (1315), unlike the shunts (1205). Magnetic screens as inFIG. 13 are generally the preferred configuration for MS Hall thrusterlayouts. However, their need to physically tie to the thruster back polemakes the components longer than shunts, leading to a higher mass, andcan impose geometric challenges for the internal layout of the thruster.

The problem with the two conventional MS Hall thruster architectures ofFIGS. 12-13 is that neither of the two configurations scale well to thelow power Hall thruster regime. The configuration of FIG. 12 is capableof only modest MS performance, while the configuration of FIG. 13results in higher magnetic circuit mass. With sub-kW operating powersand thruster outer diameters of the order of 10 cm or less, low powerHall thrusters must accommodate very high magnetic flux densities (ofthe order of 0.1-1 T) to achieve high performance, while affordingsufficient internal volume for internal components (propellantdistribution, magnet coils, etc.).

Magnetic shunts (FIG. 12) have trouble handling these levels of magneticflux, making it difficult to achieve a MS field topology at the sub-kWpower level. The use of magnetic screens (FIG. 13) can significantlylimit the internal volume available inside the thruster, driving thethruster design towards larger sizes, and therefore higher operatingpower requirements. A new geometric architecture to optimize all MS Hallthruster magnetic circuit geometries and to achieve MS for Hallthrusters operating in the low-power regime is therefore described inthe present disclosure.

The present disclosure describes a one-piece magnetic screen designwhich employs a single connection point to the magnetic circuit's backpole. The one-piece magnetic screen is capable of handling the samemagnetic flux densities as conventional magnetic screens, while reducingthe internal volume (and mass) required by the magnetic circuitcomponents. The magnetic screens are made of a magnetic material. Forexample, high permeability magnetic alloys are the most common for anyHall thruster magnetic circuit component such as the screen. MaSMi usesHiperco-50A (an Iron-Cobalt-Vanadium alloy). However, other materialsmay also include Hiperco-50 (which has slightly different chemistry thanthe 50A), VIM VAR (vacuum melted low-carbon magnetic iron), or standardmagnetic iron.

The one-piece magnetic screen is different compared to the magneticshunts and magnetic screens. The one-piece screen has an h-shapedcross-section, and it is not purely cylindrical, combining the U shapeof a magnetic shunt with a single upstream connection to the back pole.An exemplary one-piece magnetic screen implementation is illustrated inFIG. 11. The magnetic screen is illustrated as (1125), and forms asingle connection (single because of the azimuthal symmetry for thecross section of FIG. 11) with the back pole (1130). It can be notedthat the magnetic screen of FIG. 13 forms instead two connections withthe back pole. It can also be noted that the magnetic screen of FIG. 11has only one piece (it appears as two pieces only because FIG. 11 is across section with azimuthal symmetry), while the magnetic screen ofFIG. 13 has two distinct pieces. As visible in FIG. 11, the upstreamsection of the internal cathode is longitudinally longer than thedownstream section; for example, at least five times longer.

In some embodiments, the h-shaped magnetic screen therefore comprises,as visible in FIG. 11, a hollow cylinder at the upstream end, and twohollow cylinders at the downstream ends, with the two concentriccylinders joined by an annular shape corresponding to the horizontalline of the h shape.

The one-piece screen has several advantages over the use of a magneticshunt or magnetic screen, and the significance of these advantagesincreases as the thruster scale is reduced. A first advantage is thesingle connection to the back pole, which enables the one-piece magneticscreen to support the high magnetic flux densities required for MSwithout saturating. The single piece exceeds the performance of amagnetic shunt in many applications and matches the performance of apair of magnetic screens.

A second advantage is that, by using only a single connection point tothe back pole, magnetic performance is maintained with significantlymore uninterrupted internal volume available. Although the use ofmagnetic shunts yields the greatest internal volume due to their lack ofa connection to the back pole, their poor performance (especially atlower powers) reduces their applicability. The single connection pointused by the one-piece screen, ideally positioned at the outer radius ofthe screen, provides considerably more uninterrupted internal volumecompared to magnetic screens. Additionally, the reduction in materialrequired for the one-piece screen compared to conventional magneticscreens yields a lower total mass for the magnetic circuit. The outerradius position enables a greater utilization of the internal volume.

A third advantage is that the one-piece screen is a single component,and therefore has improved thermal conduction paths and improvedmagnetic coupling to the thruster. Both thermal and magnetic advantagesare achieved through fewer mechanical joints, compared to either amagnetic shunt or magnetic screens. An additional benefit of the singleintegrated component is its increased structural integrity, which isbeneficial during flight qualification environmental (shock andvibration) testing.

Therefore, as described above, a one-piece magnetic screen yields areduction of mass, an increase in structural integrity, and animprovement to the thermal design of Hall thrusters of all scales. Thelower thruster mass reduces the total mass of the propulsion subsystemand, consequently, the spacecraft dry mass. Increased structuralintegrity improves the thruster's ability to withstand vibration andshock loads imposed by launch and spacecraft separation. With totalefficiencies in the range of 40-70%, improvements to the thermal designof Hall thrusters can aid in conducting waste heat towards the keyradiating surfaces, ultimately improving thruster performance.

As visible in FIG. 11, the azimuthally-symmetrical discharge chamber hasan annular shape, the single-piece azimuthally-symmetrical magneticscreen has an h-shape cross section, the h-shape cross sectioncomprising a first prong at an upstream end and two prongs at adownstream end, the single-piece azimuthally-symmetrical magnetic screencomprises a first hollow cylinder physically contacting the back pole ata single circular point of contact, the single-pieceazimuthally-symmetrical magnetic screen comprises a second and thirdhollow cylinders, the second hollow cylinder being concentric to thethird hollow cylinder, and the azimuthally-symmetrical discharge chambercomprises a radially-outward wall and a radially-inward wall. The secondhollow cylinder of the single-piece azimuthally-symmetrical magneticscreen encircles the radially-inward wall of the azimuthally-symmetricaldischarge chamber, and the third hollow cylinder of the single-pieceazimuthally-symmetrical magnetic screen encircles the radially-outwardwall of the azimuthally-symmetrical discharge chamber, thereby forming amagnetic field protecting the radially-outward wall and theradially-inward wall of the azimuthally-symmetrical discharge chamberfrom erosion due to ion bombardment.

FIG. 28 illustrates an exemplary single-piece magnetic screen (with acut-out view), corresponding to the screen (1125) of FIG. 11. FIG. 28illustrates how the h shape cross section generates the 3D volume of thescreen by azimuthal rotation. The resulting screen shape has a firsthollow cylinder (2805) at the upstream end, contacting the back pole,and two other cylinders. One cylinder (2810) is locatedradially-outward, while the other (2815) is located radially-inward. Thedownstream ends of the cylinders have slanted edges. Each edge is slatedin the opposite direction, as visible in FIG. 28.

At the low power regime (sub-kW), a one-piece magnetic screen is anenabling feature for efficient magnetically shielded Hall thrusters. Inaddition to the benefits listed above (the most important of which isthe thermal design due to the inherently lower efficiency of lower-powerHall thrusters), the one-piece magnetic screen frees up considerablevolume inside the thruster. This facilitates and, at very low powers,enables the design and development of low-power MS thrusters.

As described above in the present disclosure, propellant flow uniformityin the discharge channel of Hall thrusters is a key contributor to thethruster performance at all power levels. Uniform propellant flowazimuthally around the discharge channel provides an evenly distributedneutral particle flux to the thruster's ionization region. The evendistribution enables a balanced thrust to be generated by the thrusteraround the full annulus of the channel, so that there are no localregions of high neutral density that could generate an asymmetric thrustvector. This uniformity also increases the probability for high levelsof propellant ionization (>90% is possible in Hall thrusters), which iscorrelated to a thruster's propellant mass utilization efficiency andcurrent utilization efficiency, and thus total efficiency. Anodemanifolds should therefore be designed to provide the most azimuthallyuniform neutral gas flow fields as possible.

The neutral gas flow field inside a Hall thruster discharge channel isproduced by the pressure difference across the anode manifold (i.e. thepropellant gas distributor). The propellant gas is supplied to the anodewith a small upstream backpressure (≤50 Torr) and flows to the dischargechamber (near vacuum). The neutral propellant density from the anodeproduces a local pressure of the order of 10 mTorr in the channel. Theinternal geometry of the anode manifold governs the distribution ofpropellant in the azimuthal direction, while the anode's exit orificeconfiguration determines the propellant's diffusivity (i.e. how wide ornarrow the propellant stream is in the radial direction). Thediffusivity is directly coupled to the propellant particle trajectoriesencouraged by the anode exit geometry. Neutral trajectories that followpredominantly radial paths rather than axial paths have a longer dwelltime in the discharge channel due to bouncing between the channel walls.This improves diffusivity by providing more time for the flow to developinto an azimuthally uniform flow field as the bulk flow moves axiallyalong the channel.

Significant efforts have been made to enhance propellant flow uniformityin Hall thruster anodes. NASA's generally accepted acceptance criteriafor an anode manifold is ±5% from the mean flow corresponding to amaximum peak-to-peak non-uniformity of ≤10%. Many contributors to poorazimuthal flow uniformity in Hall thruster anodes can be identified,including anode manifold internal geometry, manufacturing processaccuracy, manufacturing repeatability, etc. For example, the H6 anodecreates a high azimuthally uniform propellant flow field, with the threefabricated units having maximum peak-to-peak non-uniformities of 4.4%,4.6% and 7% from the mean flow. The anode manifold on NASA'snext-generation 12.5 kW HERMeS Hall thruster shares little geometricsimilarity with the H6 anode, but was intended to provide improvedpropellant flow uniformity through a conductance-balanced design.However, the HERMeS anode manifold generated a greater maximumpeak-to-peak non-uniformity than that of the H6, representing areduction in uniformity performance. A manufacturing repeatability issuewas observed for the H9 thruster, which uses the same anode design asthe H6. Three H9 anodes were produced, demonstrating maximumpeak-to-peak non-uniformities of 4.1%, 4.6%, and 9.2% at a low-flowcondition and 3.4%, 3.6%, and 6.5% at a high flow condition. While twoof the units were highly uniform and all of the units pass NASA'scriteria, the third unit was a factor of 2× less uniform than the firsttwo units.

The inability to consistently design and fabricate anode manifolds thatproduce sub-5% peak-to-peak non-uniformities represents a non-trivialproblem in Hall thruster design and development. Solving this problemwill yield higher performance from future NASA Hall thrusters. Thesolution to this problem, as described in the present disclosure, is tobuild off of the strong demonstrated performance of the H6 anodemanifold and develop a novel anode geometry that generates anexceptionally uniform flow field, while using clearly-outlinedmanufacturing processes to ensure consistency between units.

The anode manifold design that solves this problem as described in thepresent disclosure is herein called the High Uniformity Distribution(HUD) anode. The HUD anode comprises two sections. The first sectioncomprises the propellant delivery to the manifold, including tubingbetween the pressure-regulated propellant source and the anode manifold.This region is thruster-specific, simple to integrate into the anodemanifold, and arbitrary from the perspective of the anode manifolddesign. Therefore, it will not be discussed in the present disclosuresince it can be understood by the person of ordinary skill in the art.The second section is the anode manifold itself, which accepts apropellant supplied by the arbitrary propellant tube of the firstsection, and generates a highly uniform flow field downstream of theanode based on its internal geometry.

A cross-section of a Hall thruster showing the location of the anoderelative to the discharge channel (in this case, JPL's MaSMi-DM) isillustrated in FIG. 17. FIG. 17 illustrates a detail of the thruster ofFIG. 9 and FIG. 11, therefore several parts of the structure can beunderstood from the description of FIG. 9 and FIG. 11. FIG. 17highlights the axis of symmetry of the thruster (1705), as well as theanode (1710), and the discharge channel or chamber (1715). The person ofordinary skill in the art will understand that parts of the thrustersillustrated in the drawings of the present disclosure, such as forexample the discharge channel (1715) and the anode (1710), haveazimuthal symmetry along axis (1705); these are concepts readilyunderstood by the person of ordinary skill in the art and are thereforeomitted for brevity and clarity in describing the innovative features.In particular, the anode (1710) has baffles with a rectangular crosssection, as described below in the present disclosure, and has azimuthalsymmetry along axis (1705).

A key feature of anode manifolds that generate highly azimuthallyuniform flow fields is the presence of at least two azimuthal flowdistribution baffles separated by choke rings (i.e. two flat annularrings within the anode, each with a set of axial holes for gas flow topass through) prior to the anode manifold exit. The rate at which thepropellant passes from one region (i.e. baffle) inside the anode to thenext is determined by the geometry and total area of the orificesbetween the two baffles, as well as the geometry of the bafflesthemselves.

It was previously believed that the flow must be choked at each orificebecause this condition dictates a constant flow rate for a given orificegeometry and pressure difference across the orifice. However, becausepressure can vary azimuthally around the anode in a given baffle, thepressure drop across each hole on a given choke ring may not be thesame. This may lead to choked flow at some or all of the choke ringholes, but the flow rates may be different due to the variation in thepressure drops across those holes. However, recent testing hasidentified that having choked flow at all of the anode orifices is notactually a requirement.

Achieving high propellant uniformity requires for the flow resistance inthe azimuthal direction within a given baffle to be much lower than theflow resistance through the orifices out of the baffle (by an order of≥100). This requirement is expressed as a ratio of the two flowresistances. Physically, this condition enables free azimuthalpropellant flow in the baffle, until the baffle fills with gas, therebyforcing a gas flow through the axial orifices into the next baffle. Theflow resistance is inversely proportional to the flow conductance. Inthe case of the HUD anode, the azimuthal baffles have a rectangularcross section, and the orifices between baffles have a circular crosssection. As such, the flow resistances (R) and the resistance ratio canbe expressed as follows:

$\begin{matrix}{\mspace{95mu} {{R_{{circular}\mspace{11mu} {orifice}} = \frac{8\mu L_{c}}{\pi r^{4}}} {R_{rect{angular}\mspace{11mu} {annulus}} \approx \frac{12\mu L_{r}}{w{h^{3}\left( {1 - {{0.6}3\frac{h}{w}}} \right)}}}{{{Flow}\mspace{14mu} {Resistance}\mspace{14mu} {Ratio}} = {\frac{R_{{circular}\mspace{11mu} {orifice}}}{R_{rect{angular}\mspace{11mu} {annulus}}} \approx \frac{\begin{matrix}{2nL_{c}wh^{3}} \\\left( {1 - {{0.6}3\frac{h}{w}}} \right)\end{matrix}}{3\pi r^{4}L_{r}} \geq {100}}}}} & (8)\end{matrix}$

where μ is the viscosity of the propellant, L_(c) is the length of thecircular orifice, r is the radius of the circular orifice, L_(r) is themidline annular length of the rectangular annulus, w is the rectangularannulus cross section width, h is the rectangular annulus cross sectionheight, and n is the number of orifices.

In some embodiments, the number of orifices should increase movingdownstream through the anode (i.e. from one choke ring to the next), togenerate the desired pressure drop and to give a greater number ofpropellant sources to further distribute the flow azimuthally. Usingonly one set of holes does not provide sufficient propellantdistribution azimuthally around the anode, resulting in lower propellantflow uniformity. In some embodiments, the cross section of the bafflesis not rectangular, but may be chosen from different shapes, such as,for example, square, pentagonal and hexagonal. These exemplary crosssections are illustrated in FIG. 27, which shows how each adjacentbaffle has one adjacent edge (2710). Exemplary shapes are square (2715),pentagonal (2705) and hexagonal (2720).

FIG. 18 illustrates the HUD anode cross-section, as a detail of (1710)of FIG. 17. The HUD anode manifold consists of four precision-machinedinterlocking rings, each with a set of orifices with a unique size andpattern. These rings are stacked and welded or brazed together duringfinal assembly. Ring 1 (1805) is the “anode base plate” and accepts thepropellant from a supply line, such as (1720) in FIG. 17 and (1825) inFIG. 18. Ring 2 (1810) is the “upstream choke ring” and, when mated tothe anode base plate, creates a closed annular volume called the“upstream baffle.” It has a series of axially-oriented orifices designedto generate high flow resistance to the next baffle. Ring 3 (1815) isthe “downstream choke ring” and, when mated to the upstream choke ring,creates a closed annular volume called the “midstream baffle.” It alsohas a series of axially-oriented orifices designed to generate high flowresistance to the next baffle. Ring 4 (1820) is the “anode cap” and,when mated to the downstream choke ring, creates a closed annular volumecalled the “downstream baffle.” It has a series of radially-orientedorifices that are designed to encourage radial trajectories of thepropellant into the discharge channel. The design of the anode cap is akey feature of the HUD anode. FIG. 18 illustrates some exemplary holes(1830) in the anode cap (1820), oriented radially outward and inwardfrom the longitudinal axis of the anode. Multiple such holes are presentin each of the lateral sides of the baffles, which have a rectangularcross section. In some embodiments, only the last (downstream) bafflehas radially oriented holes.

Because the HUD anode is scalable depending on the Hall thruster size,the design does not have a specific number of axial and radial orifices.However, in some embodiments one or more of the following aspects of thedesign should be maintained to achieve highly uniform flow fields andconsistency in manufacturing: The flow resistance from one set oforifices to the baffle immediately upstream should be maintained at ≥100with the exception of the anode cap orifices and the downstream baffle,which are in place to generate a predominantly radial flow of thepropellant from the anode manifold; The resulting pressure ratio fromone baffle to the next at steady-state, derived from the criteria above(i.e. ≥100 flow resistance), should be maintained at ˜4; All axialorifices should have a small diameter (of the order of 0.25 mm) and havea long length-to-diameter ratio (of the order of 2:1) to encouragecontinuous flow (i.e. low Knudsen number); The anode cap should haveradial orifices (cross-drilled or offset) to direct flow radially; Theradial holes should be small in diameter, but larger than the axialholes (of the order of 0.5 mm) and have a moderate length-to-diameterratio (of the order of 1:1) to encourage a large radial component ofvelocity in the propellant flow out of the anode manifold; The anodeshould be assembled with the maximum azimuthal orifice offset betweenadjacent choke rings to prevent direct line of sight through the twosets of orifices; All orifices should be machined using EDM (electricaldischarge machining) or a similar process to ensure consistency betweeneach orifice diameter; The orifices should not be machined usingtraditional drill bits as they produce much higher variability indiameter and hole finish from orifice to orifice; The interlockingfeature of the four anode rings should be retained for simplicity andconsistency in fabrication. This feature also facilitates welding orbrazing the assembly as all component-to-component joints have externalaccess. In some embodiments, all criteria above are followed.

Using the above tenants for a high-uniformity anode manifold, theMaSMi-DM anode was designed and fabricated. Parts for five anodes werefabricated, two of which was assembled and tested to date. Prior toassembly, all of the orifices from the five sets of parts were measured.The EDM process used to make the orifices yielded <0.025 mm variancefrom orifice to orifice over all of the five sets, representingexceptional manufacturing consistency. The number and size of theorifices, the pressure ratios across each choke plate, and the flowresistance ratios across each choke plate are presented in Table 1.

TABLE 1 Orifice # of Pressure Resistance Location Diameter OrificesRatio Ratio Upstream Choke Ring 0.25 mm 8 4 540 Downstream Choke Ring0.25 mm 24 9 180 Anode Cap 0.50 mm 48 4 5.7

Two MaSMi-DM anode manifolds (SN 1 and SN 2) were fabricated and testedfor azimuthal propellant flow uniformity. Measurements of the azimuthalflow distribution for SN 1 were taken at xenon flow rates of 1 mg/s and3 mg/s. An additional flow condition of 0.5 mg/s was added for thetesting of SN 2. To ensure repeatability with the flow uniformitymeasurement, each azimuthal location was measured twice per flow rate(rotating the manifold ±360°). The azimuthal propellant distribution foranode manifolds SN 1 and SN 2 are presented in FIGS. 19-20 as the ratioof the local pressure (P) and the average azimuthal pressure (P_(mean)).FIG. 19 illustrates data for flow rates of 1 mg/s (1905) and 3 mg/s(1910). FIG. 20 illustrates data for flow rates of 0.5 mg/s (2005), 1mg/s (2010) and 3 mg/s (2015). The peak-to-peak non-uniformity of SN 1was 3.2% at 1 mg/s and 2.6% at 3 mg/s. These values decreased with SN 2,which demonstrated 2.8%, 1.5%, and 1.3% at 0.5 mg/s, 1 mg/s, and 3 mg/s,respectively. Based on these results, the HUD anode appears to be themost uniform anode manifold tested and published to date.

It should be noted that various modifications can be made to the HUDanode to improve its resilience to the non-flight environments of groundtesting. Ground test concerns for the HUD anode center around carbonthat is back-sputtered from the vacuum facility walls and that adheresto the discharge channel and anode. Risks and mitigation techniques mayinclude but are not limited to: 1. Increasing the diameter of the anodecap radial holes; and 2. Adding a lip to the downstream end of the anodecap.

Increasing the diameter of the anode cap radial holes reduces the riskof clogging due to particulate separating from the discharge channelwall. Over long-duration tests, back-sputtered carbon from a vacuumfacility can collect and subsequently separate from the dischargechannel in small clumps. Due to the clumps following the pull ofgravity, this is primarily a concern at the top (12 o'clock) position ofthe HUD anode along the outer diameter and at the bottom (6 o'clock)position of the HUD anode along the inner diameter. Because the HUDanode design does not require the orifices in the anode cap to bechoked, their diameters can be increased without compromising theneutral flow uniformity produced by the anode manifold.

Adding a lip to the downstream end of the anode cap can reduceline-of-sight of the back-sputtered carbon to the upstream portions ofthe discharge channel and anode, reducing the deposition ofback-sputtered carbon in these regions. This in turn will preventelectrical shorts between the anode and the conducting carbon coating ofthe discharge channel in long-duration tests. This modification does notchange the core functionality of the HUD anode and will still enable theproduction of a high-uniformity neutral flow. An example of thisconfiguration is shown in FIG. 21 (2105).

The HUD anode generates the most azimuthally uniform propellant flowdistribution of any Hall thruster anode tested and published to date.Furthermore, the design is simple, easily repeatable using the clearlydefined manufacturing processes above, and scalable to any thrusterpower level. An anode that generates an ultra-high azimuthally uniformpropellant flow field has the potential to improve thruster totalefficiency by several percentage points when compared to less uniformanodes (accomplished by improving the mass and current utilizationefficiencies). High uniformity flow fields can generate thrust vectorsthat are more closely aligned with the thruster's centerline axis,reducing the need for gimbal compensation in flight. Because the anodemass is largely dependent on the Hall thruster power level and varies byvery small amounts within that given power level, there is no or littlemass penalty for using the proposed HUD anode. By standardizing themachining process of the anodes and using highly consistent machiningpractices, the unit-to-unit variability can be minimized. Since the HUDanode is not dependent on thruster power level, it is widely applicableto all Hall thruster power regimes.

As known to the person of ordinary skill in the art, Hall thrusters aregenerally azimuthally symmetric with the primary region of the anode ormanifold being annular in shape. The axis of symmetry in the drawings ofthe present disclosure will be readily understood by the person ofordinary skill in the art.

As described above, the cross-sections of the baffles that form theanode are rectangular. FIG. 22 illustrates exemplary rectangular crosssection baffles (2205), each of them being an annular ring. These ringsare adjacent, and in this example for three consecutive spaces forpropellant flow with a rectangular cross section (2220). The propellantis supplied by one or more supply lines (2225). For example, threesupply lines may be used. Each supply line supplies propellant gas inthe first baffle. The gas moves between consecutive baffles throughcircular openings. One or more circular openings may connect adjacentbaffles. For example, if three supply lines are used, three circularopenings may be used. The openings are not aligned with each other inconsecutive baffles, to form a discontinuous path between the firstbaffle attached to the supply line, and the anode cap. The misalignmentencourages azimuthal uniformity for the gas flow. In some embodimentsthe circular holes are equally spaced within the same baffle, and havethe maximum offset possible with respect to the adjacent baffles. Forexample, if there are three circular axial holes, they can be placed120° apart; if the next baffle also has three axial holes, these couldbe placed 120° with respect to each other, but offset by 60° relative tothe previous set of holes.

FIG. 22 illustrates multiple holes in the anode cap, in particularpointing radially inward (2210) from the central longitudinal axis ofthe anode, and radially outward (2215). Comparing FIG. 22 and FIG. 23,can be noted that the radial holes (2210, 2215) are larger than theaxial holes between baffles (2305). The radial holes (2210, 2215) may becircular or have other shapes. The axial holes (2305) may be circular orhave other shapes as well. FIG. 23 illustrates exemplary circular holesconnecting adjacent baffles (2305), as well as axial holes (2310). FIG.23 also illustrates a larger axial hole (2315) used for the supply lineconnecting to the first baffle, upstream. One or more of such largeraxial holes may be used to connect to the supply line. In someembodiments, the total surface area of the holes connecting to thesupply line is larger than that of the holes connecting the first andsecond baffles, and larger than the holes connecting the second andthird (most downstream) baffle. Similar arrangements can be made if twoor more than three baffles are used. The radial holes have a total arealarger than the holes connecting the downstream baffles.

The examples set forth above are provided to those of ordinary skill inthe art as a complete disclosure and description of how to make and usethe embodiments of the disclosure, and are not intended to limit thescope of what the inventor/inventors regard as their disclosure.

Modifications of the above-described modes for carrying out the methodsand systems herein disclosed that are obvious to persons of skill in theart are intended to be within the scope of the following claims. Allpatents and publications mentioned in the specification are indicativeof the levels of skill of those skilled in the art to which thedisclosure pertains. All references cited in this disclosure areincorporated by reference to the same extent as if each reference hadbeen incorporated by reference in its entirety individually.

It is to be understood that the disclosure is not limited to particularmethods or systems, which can, of course, vary. It is also to beunderstood that the terminology used herein is for the purpose ofdescribing particular embodiments only, and is not intended to belimiting. As used in this specification and the appended claims, thesingular forms “a,” “an,” and “the” include plural referents unless thecontent clearly dictates otherwise. The term “plurality” includes two ormore referents unless the content clearly dictates otherwise. Unlessdefined otherwise, all technical and scientific terms used herein havethe same meaning as commonly understood by one of ordinary skill in theart to which the disclosure pertains.

What is claimed is:
 1. A Hall thruster comprising: a center axisoriented from an upstream section of the Hall thruster, the upstreamsection housing a back pole for a magnetic circuit and a supply line fora gas propellant, to a downstream section concentric with anazimuthally-symmetrical discharge chamber; and an internally-mountedcathode along the center axis, the internally-mounted cathode comprisingan upstream section and a downstream section, wherein: a diameter of thedownstream section of the internally-mounted cathode is larger than adiameter of the upstream section of the internally-mounted cathode, andan axial length of the upstream section of the internally-mountedcathode is larger than an axial length of the downstream section of theinternally-mounted cathode.
 2. The Hall thruster of claim 1, whereinsaid axial length of the upstream section is at least five times largerthan said axial length of the downstream section.
 3. The Hall thrusterof claim 1, wherein the Hall thruster further comprises an electronemitter that is housed in the downstream section of theinternally-mounted cathode.
 4. The Hall thruster of claim 1, wherein theHall thruster further comprises a keeper electrode assembly that ishoused in the downstream section of the internally-mounted cathode 5.The Hall thruster of claim 1, wherein the Hall thruster furthercomprises cathode propellant and/or electrical distribution lines housedin the upstream section of the internally-mounted cathode.
 6. The Hallthruster of claim 1, wherein the Hall thruster further comprises cathodepropellant and/or electrical distribution lines formed via respectiveholes in an inner core of the Hall thruster parallel to the upstreamsection of the internally-mounted cathode.
 7. The Hall thruster of claim1, wherein the internally-mounted cathode is arranged within a hollowspace formed, along the center axis, in an inner core of the Hallthruster.
 8. The Hall thruster of claim 7, wherein the hollow spaceincludes a counterbore that defines the larger diameter of thedownstream section of the internally-mounted cathode.
 9. The Hallthruster of claim 1, further comprising a single-pieceazimuthally-symmetrical magnetic screen, wherein: theazimuthally-symmetrical discharge chamber has an annular shape, and thesingle-piece azimuthally-symmetrical magnetic screen has an h-shapecross section, the h-shape cross section comprising a first prong at anupstream end and two prongs at a downstream end.
 10. The Hall thrusterof claim 1, wherein the downstream section of the internally-mountedcathode comprises a cathode heater.
 11. The Hall thruster of claim 1,wherein the downstream section of the internally-mounted cathode isheaterless.
 12. A method for increasing cross-sectional area of a centercore in a magnetically shielded (MS) Hall thruster, the methodcomprising: forming a downstream bore in a center core of the MS Hallthruster along a center axis of the MS Hall thruster; forming anupstream bore in the center core of the MS Hall thruster along thecenter axis of the MS Hall thruster, the downstream bore having: adiameter that is larger than a diameter of the upstream bore, and alength along the center axis that is shorter than a length along thecenter axis of the upstream bore; based on the forming, forming acounterbore that defines a downstream section of an internally-mountedcathode of the MS Hall thruster, the downstream section having adiameter that is larger than a diameter of an upstream section of theinternally-mounted cathode; and based on the forming, providing adiameter of the center core at the upstream section of theinternally-mounted cathode that is larger than a diameter of the centercore at the downstream section of the internally-mounted cathode,thereby increasing the cross-sectional area of the center core.
 13. Themethod according to claim 12, wherein a length along the center axis ofthe upstream bore is at least five times larger than a length of thedownstream bore along the center axis.
 14. The method according to claim12, wherein: the MS Hall thruster is a low-power magnetically shieldedHall thruster, and the increasing of the cross-sectional area of thecenter core increases magnetic flux and reduces magnetic saturation. 15.A Hall thruster comprising: a center axis oriented from an upstreamsection of the Hall thruster, the upstream section housing a back polefor a magnetic circuit and a supply line for a gas propellant, to adownstream section concentric with an azimuthally-symmetrical dischargechamber; and an internally-mounted cathode along the center axis, theinternally-mounted cathode comprising an upstream section and adownstream section, wherein: a diameter of the downstream section of theinternally-mounted cathode is larger than a diameter of the upstreamsection of the internally-mounted cathode, and an axial length of theupstream section of the internally-mounted cathode is different from anaxial length of the downstream section of the internally-mountedcathode.